Asymptotic arc-components of unimodal inverse limit spaces

We consider the inverse limit space (I,f) of a unimodal bonding map f as fixed bonding map. If f has a periodic turning point, then (I,f) has a finite non-empty set of asymptotic arc-components. We show how asymptotic arc-components can be determined from the kneading sequence of f. This gives an alternative to the substitution tiling space approach taken by Barge and Diamond [Ergodic Theory Dynamical Systems 21 (2001) 1333].     

Class field theory for strictly quasilocal fields with Henselian discrete valuations

The paper establishes a relationship between finite separable extensions and norm groups of strictly quasilocal fields with Henselian discrete valuations, which yields a generally nonabelian one-dimensional local class field theory.     

Handling of intrinsic divergence in the orthogonal gradient method of orbital optimization in an MC-SCF framework and geometry optimization in pathological cases: I (propynal in excited states)

It is demonstrated that a generalized version of the orthogonal gradient method of orbital optimization may sometimes encounter a specific divergence problem which may be termed intrinsic to the first order method. Instead of switching over to a more sophisticated second order method one can cure the divergence problem at the first order level itself by suitably tailoring the MC-SCF operator or the MC-SCF energy matrix. Results of complete geometry optimization of propynal in^l,3nπ* and³ππ* states (pathological cases) are reported to demonstrate the usefulness of the method at an INDO-MCSCF level of approximation. The results of structure calculations are further rationalized from generalized quantum chemical bond order indices.     

Homogeneous endpoint Besov space embeddings by Hausdorff capacity and heat equation

Two embeddings of a homogeneous endpoint Besov space are established via the Hausdorff capacity and the heat equation. Meanwhile, a co-capacity formula and a trace inequality are derived from the Besov space.     

Polymer synthesis in the presence of bis(cyclopentadienyl) derivatives of Group IV–VI transition metal dichlorides: a quantum chemical study of particular reaction stages

Key pathways of interaction between growing radicals of vinyl monomers and bis(cyclopentadienyl) derivatives of Group IV–VI transition metal dichlorides were studied by the BP86/6-31G(d) and B3LYP/LanL2DZ quantum chemical methods. Prospects for use of these organometallic compounds as chain growth regulators in controlled polymerization were assessed. The character of the interaction of the compounds studied with the growing radicals is mainly determined by the metal atom. Dedicated to Academician G. A. Abakumov on the occasion of his 70th birthday. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1690–1694, September, 2007.     

Input optimization: I. Optimal realizations of mathematical models

Mathematical models are considered as input-output systems. The input is data (technological coefficients, available energy, prices) and the output is the feasible set, the set of optimal solutions, and the optimal value. We study when output is a continuous function of input and identify optimal (minimal) realizations of mathematical models. These are states of the model having the property that every stable perturbation of input results in a locally worse (higher) value of the optimal value function. In input optimization we “optimize” mathematical model rather than a specific mathematical program. This research was supported in part by the Natural Sciences and Engineering Research Council of Canada, and in part by the Gouvernement du Québec, programme de formation de chercheurs et d’action concertée.     

Rotational diffusion of dyes in solvents of low viscosity from transient-dichroism experiments

Rotational diffusion data from pulsed laser experiments are presented for dye molecules dissolved in alcohols and non-alcohols. Cresyl violet and fluorescein both exhibit strong dependence of the rotational motion upon solvent molecular structure. In complete contrast the rotational diffusion of the oblong dyes pyronine G and acridine orange do not reveal any specific solute-solvent interaction.     

Solvent effects on the electronic spectra of oxovanadium(IV) β-diketonates comments on the papers of ebraheem et al.

Summary Solvent effects on the electronic absorption spectra of oxovanadium(IV) 31/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-diketonates are discussed. It has been found that positions of the long-wave-length bands can be described in terms of the donor-acceptor concept including the donor numbers and the acceptor numbers.

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Lösungsmitteleffekte bei den Elektronenspektren von Oxovanadium(IV)-31/xhuge946.gif" alt="beta" align="MIDDLE" BORDER="0">-diketonaten. Kommentar zu den Arbeiten von Ebraheem et al. (Kurze Mitt.)

Zusammenfassung Es werden Lösungsmitteleffekte bei den Elektronenspektren von Oxovanadium(IV)-31/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-diketonaten diskutiert. Dabei wurde gefunden, daß die Lage der langwelligen Banden auf Basis eines Donor-Akzeptor-Modells unter Berücksichtigung der Donor- und Akzeptor-Nummern beschrieben werden kann.

     

Salze von Halogenophosphorsäuren XIX [1] Über die Bildung und den Nachweis stabiler Intermediate bei der Reaktion von Fluorid mit Phosphoroxidchlorid

Salts of Halogenophosphoric Acids. XIX Formation and Identification of Stable Intermediates on the Reaction of Fluoride with Phosphorus Oxychloride By reaction of POCl₃ with fluorides of tertiary amines in the presence of the free amines the oxo-fluorophosphates [F₂P(O? O? PF₅)]^?, [OPF₅]^2?, and [OPF₄]^? are formed as intermediates on the way to [PF₆]^?. The compounds were characterized by NMR spectroscopy.     

Characterization of the disordered phosphate network in CaO-P2O5 glasses by P solid-state NMR and Raman spectroscopies

In this study, the disordered network of calcium phosphate glasses is investigated by Raman scattering and ³¹P magic angle spinning (MAS) solid-state NMR spectroscopies. The use of both spectroscopies in a combined approach allows drawing a detailed understanding of the structure of these glasses. The P―O―P connectivity between successive PO₄ tetrahedra is probed using through-bond double quantum-single quantum (DQ-SQ) and triple quantum-single quantum (TQ-SQ) MAS NMR correlation experiments. Over the broad range of glass compositions studied here, two very different phosphate network topologies are encountered. The results obtained for the polyphosphate compositional range (above 50 mol% Ca) allow determining the phosphate chain-length distribution in the glass as a function of the modifier cation content. For the ultraphosphate region (below 50 mol% Ca), the network topology undergoes a sudden change close to 39 mol% Ca which can be interpreted in terms of a rigidity transition.